Between the shaft rotates with zero torque, thus there will be no acceleration ω 2 = ω 3 . Between , a constant output torque is applied causing the flywheel to slow down from ω 3 to ω 4 .
Shigley’s Mechanical Engineering Design, 9 th Ed. Class Notes by: Dr. Ala Hijazi Ch.16 Page 12 of 13 The work input to the flywheel is: And the work output is: - If then . - If then . - If then The work done on the flywheel between can also be found as the difference in kinetic energy . Most of the torque-angular position functions encountered in engineering application are so complicated and they require using numerical integration to find the total work ( area under the curve ). Fig 18-28 shows the torque of a one cylinder engine for one cycle. Integrating the curve gives the total energy supplied by the engine. Then dividing the result by the length of one-cycle ( 4π ) gives the mean torque value of the engine. The allowable range of speed fluctuation is usually defined using the “ Coefficient of speed fluctuation ” : where ω is the nominal angular velocity: Substitute in the energy difference equation we get: where is the area under the torque curve This equation can be used to obtain the flywheel inertia “ ” needed to satisfy the required value.
Shigley’s Mechanical Engineering Design, 9 th Ed. Class Notes by: Dr. Ala Hijazi Ch.16 Page 13 of 13 See Example 16-6 from text
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